1. Field of the Invention
The invention provides a method and related apparatus for digital-analog conversion, and more particularly, a digital-analog conversion system for achieving better dynamic element matching in an over-sampling D/A converter.
2. Description of the Prior Art
Due to the advancing techniques of semiconductor, a variety of information, data, characters, and audio data are capable of being processed and delivered quickly. Various electrical circuits for signal processing become essential hardware of today's information society. Digital-analog converter systems capable of converting digital signals into analog signals have found a myriad of applications in many electrical circuits produced for communication, audiovisuals, and hi-fi equipment uses.
D/A converter systems are divided into two classes: Nyquist sampling rate D/A converter systems and over-sampling D/A converter systems. As known, an ideal sampling rate (Nyquist sampling rate) is at least greater than twice the signal frequency when sampling. This is the so-called sampling law. A D/A converter system designed based on this sampling rate is called a Nyquist D/A converter system. However, sigma-delta converters, which are developing quickly recently, is an over-sampling D/A converter system. In this kind of system, a sampling rate is further greater than that in the Nyquist sampling rate D/A converter system.
Generally speaking, a D/A converter system includes a core digital-analog circuit and related converter control logic for generating a corresponding analog output according to a digital input. The digital-analog circuit includes a plurality of switch elements capable of selectively supplying a unit of electricity or not. While generating a corresponding analog output, the numbers of switch elements which are turned on are determined according to the digital input. For example, if the digital input is a binary 011 (which equals three), then three switch elements are turned on and the others are turned off to supply three units of electricity as the analog output of the digital-analog circuit.
In some digital-analog applications, the value of digital input is positive or negative. Correspondingly, in such digital-analog applications, each switch element is capable of selectively supplying a unit of positive electricity or a unit of negative electricity or neither to represent the digital value of +1, −1, or 0 respectively. In the prior art, if the digital input is +4, the digital-analog circuit turns on four switch elements for supplying a total of four units of positive electricity; if the digital input is −2, the digital-analog circuit turns on two switch elements for supplying a total of two units of negative electricity. The switch elements are called three-level switch elements due to being capable of selectively supplying a unit of positive electricity or a unit of negative electricity or no electricity.
Three-level switch elements are realized practically by using switch capacitors or positive/negative current source techniques. In the switch capacitor technique, the switch elements include a capacitor for selectively supplying a unit of positive electricity or a unit of negative electricity or no electricity. In the positive/negative current source technique, the switch elements include two current sources for supplying a two-way current. One current source is connected and the other is disconnected for selectively supplying a unit of positive electricity or a unit of negative electricity, and both current sources are connected or disconnected for supplying no electricity. However, no matter what technique is applied in such digital-analog circuits, there are still mismatches between switch elements. Each switch element in the digital-analog circuit supplies a unit of positive electricity or negative electricity in an ideal condition, but different switch elements practically supply different electricity causing mismatch due to manufacturing differences. For example, in actuality one switch element may supply 1.05 units of electricity and another may supply 0.98 units of electricity, making the electricity of the compound analog output unequal to the ideal value and thus causing a mismatch.
Besides mismatch error, the switch elements still have gain error. Generally speaking, there is mismatch between the positive and negative electricity provided by each three-level switch element. Ideally, each three-level switch element is capable of selectively supplying a unit of positive electricity or a unit of negative electricity. But in practice, even the positive or negative electricity provided by the same switch element are marginally different. For example, one three-level switch element supplies 1.02 units of positive electricity but merely supplies 0.96 units of negative electricity, thus causing gain error. When the switch element supplies 1.02 units of positive electricity according to the digital input value of +1, the gain error is 1.02/1; but when the switch element supplies 0.96 units of negative electricity according to the digital input value of −1, the gain error is 0.96/1. This represents that the switch element has gain error when supplying electricity according to positive or negative digital input. In the positive/negative current source technique, the three-level switch elements have bigger gain error. Because the positive and negative current sources are realized with different type of transistors (NMOS and PMOS) in the same switch element, it is difficult to reach a balance and match the positive and negative current sources.
With regard to the mismatch between the switch elements, some prior art already lower the effects. For example, when using an over-sampling D/A converter system, a known D/A converter circuit uses different switch elements to generate an analog output for reducing the mismatch effect between switch elements, which is so called dynamic element matching technique.
However, the prior art does not readily lower the gain error caused by the imbalance of each switch element's positive and negative electricity. Most D/A converter systems lower the mismatch between switch elements, but are unable to solve the gain error. This reduces the immunity against errors, so known digital-analog converter systems are unable to get a better signal-noise ratio (SNR).